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The Cournot-Bertrand profit differential: A Reversal result in network goods duopoly

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  • Rupayan Pal

    ()
    (Indira Gandhi Institute of Development Research)

Abstract

We revisit the classic profit-ranking of Cournot and Bertrand equilibria and the issue of endogenous choice of a price or a quantity contract, but for a network goods duopoly. We show that, if network externalities are strong (weak), each firm earns higher (lower) profit under Bertrand competition than under Cournot competition. Therefore, unless network externalities are weak, the classic profit-ranking is reversed. When modes of product market competition are endogenously determined, Cournot equilibrium always constitutes the subgame perfect Nash equilibrium (SPNE). However, a prisoners's dilemma type of situation arises and the SPNE is Pareto inefficient, unless network externalities are weak.

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Paper provided by Indira Gandhi Institute of Development Research, Mumbai, India in its series Indira Gandhi Institute of Development Research, Mumbai Working Papers with number 2013-014.

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Length: 17 pages
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Handle: RePEc:ind:igiwpp:2013-014

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Keywords: Network externalities; Cournot; Bertrand; Profit ranking; Endogenous mode of competition;

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  1. Dastidar, Krishnendu Ghosh, 1997. "Comparing Cournot and Bertrand in a Homogeneous Product Market," Journal of Economic Theory, Elsevier, vol. 75(1), pages 205-212, July.
  2. Luciano Fanti & Nicola Meccheri, 2011. "The Cournot-Bertrand profit differential in a differentiated duopoly with unions and labour decreasing returns," Economics Bulletin, AccessEcon, vol. 31(1), pages 233-244.
  3. Economides, Nicholas, 1996. "Network externalities, complementarities, and invitations to enter," European Journal of Political Economy, Elsevier, vol. 12(2), pages 211-233, September.
  4. Symeonidis, George, 2003. "Comparing Cournot and Bertrand equilibria in a differentiated duopoly with product R&D," International Journal of Industrial Organization, Elsevier, vol. 21(1), pages 39-55, January.
  5. Tanaka, Yasuhito, 2001. "Profitability of price and quantity strategies in an oligopoly," Journal of Mathematical Economics, Elsevier, vol. 35(3), pages 409-418, June.
  6. Scrimitore, Marcella, 2013. "Price or quantity? The strategic choice of subsidized firms in a mixed duopoly," Economics Letters, Elsevier, vol. 118(2), pages 337-341.
  7. Leonard Cheng, 1985. "Comparing Bertrand and Cournot Equilibria: A Geometric Approach," RAND Journal of Economics, The RAND Corporation, vol. 16(1), pages 146-152, Spring.
  8. Ghosh, Arghya & Mitra, Manipushpak, 2010. "Comparing Bertrand and Cournot in mixed markets," Economics Letters, Elsevier, vol. 109(2), pages 72-74, November.
  9. Piercarlo Zanchettin, 2006. "Differentiated Duopoly with Asymmetric Costs," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 15(4), pages 999-1015, December.
  10. Tasnadi, Attila, 2006. "Price vs. quantity in oligopoly games," International Journal of Industrial Organization, Elsevier, vol. 24(3), pages 541-554, May.
  11. Häckner, Jonas, 1999. "A Note on Price and Quantity Competition in Differentiated Oligopolies," Research Papers in Economics 1999:9, Stockholm University, Department of Economics.
  12. Okuguchi, Koji, 1987. "Equilibrium prices in the Bertrand and Cournot oligopolies," Journal of Economic Theory, Elsevier, vol. 42(1), pages 128-139, June.
  13. Kangsik Choi, 2012. "Price And Quantity Competition In A Unionised Mixed Duopoly: The Cases Of Substitutes And Complements," Australian Economic Papers, Wiley Blackwell, vol. 51(1), pages 1-22, 03.
  14. Miller, Nolan H & Pazgal, Amit I, 2001. "The Equivalence of Price and Quantity Competition with Delegation," RAND Journal of Economics, The RAND Corporation, vol. 32(2), pages 284-301, Summer.
  15. Dixit, Avinash K., 1978. "A Model of Duopoly Suggesting a Theory of Entry Barriers," The Warwick Economics Research Paper Series (TWERPS) 125, University of Warwick, Department of Economics.
  16. Hoernig, Steffen, 2012. "Strategic delegation under price competition and network effects," Economics Letters, Elsevier, vol. 117(2), pages 487-489.
  17. Katz, Michael L & Shapiro, Carl, 1985. "Network Externalities, Competition, and Compatibility," American Economic Review, American Economic Association, vol. 75(3), pages 424-40, June.
  18. Matsumura, Toshihiro & Ogawa, Akira, 2012. "Price versus quantity in a mixed duopoly," Economics Letters, Elsevier, vol. 116(2), pages 174-177.
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